A search for the rare decay D$^0$$\to$$\mu^+\mu^-$ is reported using proton-proton collision events at $\sqrt{s}$ = 13.6 TeV collected by the CMS detector in 2022$-$2023, corresponding to an integrated luminosity of 64.5 fb$^{-1}$. This is the first analysis to use a newly developed inclusive dimuon trigger, expanding the scope of the CMS flavor physics program. The search uses D$^0$ mesons obtained from D$^{*+}$$\to$ D$^0\pi^+$ decays. No significant excess is observed. A limit on the branching fraction of $\mathcal{B}$(D$^0$$\to$$\mu^+\mu^-$) $\lt$ 2.4 $\times$ 10$^{-9}$ at 95% confidence level is set. This is the most stringent upper limit set on any flavor changing neutral current decay in the charm sector.
Summary of branching fraction.
Summary of systematic uncertainties for the D->mumu branching fraction measurement with their corresponding contributions in the signal channel.
The distributions of the dipion invariant mass $m_{\pi\pi}$ for the normalization channel in data.
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